Complex Systems 535, Winter 2004: Network Theory

Description:

This course will introduce and develop the mathematical theory of networks,
particularly social and technological networks, with applications to
important network-driven phenomena in epidemiology of human infections and
computer viruses, the Internet, network resilience, web search engines, and
many others.

Topics to be covered will include experimental studies of social networks,
the world wide web, information and biological networks; methods and
computer algorithms for the analysis and interpretation of network data;
graph theory; models of networks including random graphs, preferential
attachment models, and the small-world model; computer simulation methods;
network dynamics.

A provisional outline of the course can be found here. Details may change, but this is reasonably
accurate.

Requirements

Students should have studied calculus and linear algebra before taking the
course, and should in particular be comfortable with the solution of linear
differential equations and with the calculation and properties of
eigenvalues and eigenvectors of matrices. In addition, a moderately large
portion of the course, perhaps three weeks, will deal with computer methods
for studying networks. Although students will not be required to write
computer programs, some experience with computer programming will be a
great help in understanding this part of the course.

Coursework

In addition to reading assignments, there will be weekly graded problem
sets, consisting both of theory questions and of problems demonstrating
applications of theory to example networks. There will be one mid-term and
a final. The final will be on Friday, April 23 from 1:30pm till 3:30pm.
Grade will be 40% on the homeworks, 25% on the mid-term, and 35% on the
final.

Resources

There is no set text for this course because no one has written one
yet. But there is a course-pack as described below, and we may read some
research papers that address particular topics during the course. There
are also a number of books that cover parts of the material quite well.

Course-pack: The course-pack contains a copy of the review article
The structure and function of complex networks,
M. E. J. Newman, SIAM Review45, 167-256 (2003). Copies of
the course-pack are available from Howard Oishi in the Complex Systems
office (4485 Randall).

Books: A list of useful books is given below. None of them
is required. However, if you want recommendations, I'd recommend for
graph theory either Wilson (introductory) or West (more advanced), and for
social network analysis either Scott or Wasserman & Faust. The Ahuja book
is excellent if you're interested in the computer programming/algorithms
side of things. Meyer is good if you need to brush up on your linear
algebra.

Related courses: Here is a list of courses taught here and elsewhere
that deal with related topics. Many of these web sites contain useful
material, such as bibliographies or collections of relevant articles.